Energy Independent Estimation of the Equivalent Stationary Duration of Earthquake Accelerograms

The equivalent stationary duration of an earthquake time history is one of the most important parameter in the characterization of a seismic record. This parameter and his intensity value are strongly related to the non-linear behavior of both a structure and its foundation soil. The importance of this time quantity comes from the fact that its estimation implies the complete identification of the part of a seismic signal having higher energy content in terms of both time length (duration) and position along the time axis with the corresponding mean intensity value. Three alternative procedures for the estimation of the equivalent stationary duration parameter are here proposed. These definitions have the common character of being independent from any global or local value of the energy released during the strong ground motion. Two of them comes directly from commonly used signal analysis relations while the other is strictly related to the fundamental definition of stationary and amplitude modulated stochastic process; all the examined definitions share the same time positioning procedure. Particular attention is also devoted to investigating the effectiveness of the different formulations with regard to the linear elastic response of a single degree of freedom oscillator. In particular the advantage of each of the examined durations is pointed out in terms of the response spectra obtained for the natural record compared to the ones acquired using just the equivalent stationary part of the record extracted employing a common type of tapering window. The numerical example is based on two natural records that can be considered as representative samples extracted from two of the most significant seismic Italian events of the last forty years